Alexei Onatski

Determining the number of factors from empirical distribution of eigenvalues

We develop a new estimator of the number of factors in the approximate factor models. The estimator works well even when the idiosyncratic terms are substantially correlated. It is based on the fact, established in the paper, that any finite number of the largest idiosyncratic eigenvalues of the sample covariance matrix cluster around a single point. In contrast, all the systematic eigenvalues, the number of which equals the number of factors, diverge to infinity. The estimator consistently separates the diverging eigenvalues from the cluster and counts the number of the separated eigenvalues. We consider a macroeconomic and a financial application.

TESTING HYPOTHESES ABOUT THE NUMBER OF FACTORS IN LARGE FACTOR MODELS

In this paper we study high-dimensional time series that have the generalized dynamic factor structure. We develop a test of the null of k 0 factors against the alternative that the number of factors is larger than k 0 but no larger than k 1 >k 0 . Our test statistic equals max k 0 >klk 1 (Gamma k - Gamma k+1 )(Gamma k+1 - Gamma k+2 ), where Gamma i is the ith largest eigenvalue of the smoothed periodogram estimate of the spectral density matrix of data at a prespecified frequency. We describe the asymptotic distribution of the statistic, as the dimensionality and the number of observations rise, as a function of the Tracy-Widom distribution and tabulate the critical values of the test. As an application, we test different hypotheses about the number of dynamic factors in macroeconomic time series and about the number of dynamic factors driving excess stock returns. Copyright 2009 The Econometric Society.

Robust Monetary Policy Under Model Uncertainty in a Small Model of the U.S. Economy

This paper examines monetary policy in Rudebusch and Svenssons (1999) two equation macroeconomic model when the policymaker recognizes that the model is an approximation and is uncertain about the quality of that approximation. It is argued that the minimax approach of robust control provides a general and tractable alternative to the conventional Bayesian decision theoretic approach. Robust control techniques are used to construct robust monetary policies. In most (but not all) cases, these robust policies are more aggressive than the optimal policies absent model uncertainty. The specific robust policies depend strongly on the formation of model uncertainty used, and we make some suggestions about which formulation is most relevant for monetary policy applications.

Asymptotic power of sphericity tests for high-dimensional data

This paper studies the asymptotic power of tests of sphericity against perturbations in a single unknown direction as both the dimensionality of the data and the number of observations go to infinity. We establish the convergence, under the null hypothesis and the alternative, of the log ratio of the joint densities of the sample covariance eigenvalues to a Gaussian process indexed by the norm of the perturbation. When the perturbation norm is larger than the phase transition threshold studied in Baik et al. (2005), the limiting process is degenerate and discrimination between the null and the alternative is asymptotically certain. When the norm is below the threshold, the process is non-degenerate, so that the joint eigenvalue densities under the null and alternative hypotheses are mutually contiguous. Using the asymptotic theory of statistical experiments, we obtain asymptotic power envelopes and derive the asymptotic power for various sphericity tests in the contiguity region. In particular, we show that the asymptotic power of the Tracy-Widom-type tests is trivial, whereas that of the eigenvalue-based likelihood ratio test is strictly larger than the size, and close to the power envelope.

The Tracy–Widom limit for the largest eigenvalues of singular complex Wishart matrices

This paper extends the work of El Karoui [Ann. Probab. 35 (2007) 663--714] which finds the Tracy--Widom limit for the largest eigenvalue of a nonsingular

Signal detection in high dimension: The multispiked case

p

DETECTION OF WEAK SIGNALS IN HIGH-DIMENSIONAL COMPLEX-VALUED DATA

-dimensional complex Wishart matrix

Factor Analysis of a Large DSGE Model

W_{\mathbb{C}}(\Omega_p,n)

Extreme canonical correlations and high-dimensional cointegration analysis

to the case of several of the largest eigenvalues of the possibly singular

Group invariance, likelihood ratio tests, and the incidental parameter problem in a high-dimensional linear model

(n<p)